Answer:
see attached
Step-by-step explanation:
The leading coefficient of this cubic (odd-degree) function is negative, so the overall shape of the curve will be downward-sloping (\). The zeros of the factors are at x=-6 and x=0 (multiplicity 2), so we know the first crossing of the x-axis will occur at x=-6. The graph will touch, but not cross, the x-axis at x=0 and continue descending from there.
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The local minimum will be located 2/3 of the way from the "touch" point to the other x-intercept, so is at x=-4. The value of the function there is ...
y = -(-4)²(-4+6) = -32
The graph is symmetrical about the inflection point halfway between the local extremes, which point is (-2, -16). Then another point on the curve will be 6 units to the right of the local minimum, at (2, -32).
